An object travels on a line and has velocity function over time

$v(t)=t(t-2)$

The total displacement between $t=0$ and $t=$a can be calculated as

${\displaystyle \underset{0}{\overset{a}{}}}v(t)dt$

$={\displaystyle \underset{0}{\overset{a}{}}}t(t-2)dt$

$=({\displaystyle \underset{0}{\overset{a}{}}}tdt)({\displaystyle \underset{0}{\overset{a}{}}}(t-2)dt)$

$=(\frac{1}{2}{t}^2)(\frac{1}{2}{t}^2-2t){|}_0^a|$

$=(\frac{1}{2}{a}^2)(\frac{1}{2}{a}^2-2a)$

True

False